{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PKU6MRCIFCPXRTDIVYWYO6OJNB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"84b549ae5bdda222f328a879213ea60f3d4bb308cdf8de4dcf57a0d44b025922","cross_cats_sorted":["hep-th","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-15T19:53:27Z","title_canon_sha256":"958971126764970b4dc00cd9b1dcc9f4254204ed066b55655022839e12517929"},"schema_version":"1.0","source":{"id":"1303.3882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3882","created_at":"2026-05-18T01:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3882v1","created_at":"2026-05-18T01:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3882","created_at":"2026-05-18T01:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"PKU6MRCIFCPX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKU6MRCIFCPXRTDI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKU6MRCI","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1023eff61e56acda29bd5c1cbd2a9fc64126225478c45f7a5dc94061ecd90861","target":"graph","created_at":"2026-05-18T01:51:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We show that the refined Donaldson-Thomas invariants of C3, suitably normalized, have a Gaussian distribution as limit law. Combinatorially these numbers are given by weighted counts of 3D partitions. Our technique is to use the Hardy-Littlewood circle method to analyze the bivariate asymptotics of a q-deformation of MacMahon's function. The proof is based on that of E.M. Wright who explored the single variable case.","authors_text":"Andrew Morrison","cross_cats":["hep-th","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-15T19:53:27Z","title":"A Gaussian distribution for refined DT invariants and 3D partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3882","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8f65f6327537a04a46a2797a328e98cb7e8033a1949f0e8b1686d6e28f390077","target":"record","created_at":"2026-05-18T01:51:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"84b549ae5bdda222f328a879213ea60f3d4bb308cdf8de4dcf57a0d44b025922","cross_cats_sorted":["hep-th","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-15T19:53:27Z","title_canon_sha256":"958971126764970b4dc00cd9b1dcc9f4254204ed066b55655022839e12517929"},"schema_version":"1.0","source":{"id":"1303.3882","kind":"arxiv","version":1}},"canonical_sha256":"7aa9e64448289f78cc68ae2d8779c9687ade757b66cf055f88eac9b7afd85eef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aa9e64448289f78cc68ae2d8779c9687ade757b66cf055f88eac9b7afd85eef","first_computed_at":"2026-05-18T01:51:06.704633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:06.704633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AcBqRokL/yb6eNuBrfCkcf+Lw/kDgTAIwugU78Pdzaf/n4Hn17F986W3Of1vHd1Kr4iH1Sb5njmCo7lXifw5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:06.705221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f65f6327537a04a46a2797a328e98cb7e8033a1949f0e8b1686d6e28f390077","sha256:1023eff61e56acda29bd5c1cbd2a9fc64126225478c45f7a5dc94061ecd90861"],"state_sha256":"1714dbd519e1a47fef2d7c27ae7a9d0fb9320a5deabe3ad1a8c2c1bcc1221ddc"}